A Discourse on the Drinking Bird G. K. Vemulapalll University of Arizona, Tucson, AZ 85721 There is a simple, inexpensive device that clearly demonstrates the unique reasoning used in thermodynamics, illustrates the principles behind phase transitions and heat engines, and provides very interesting material for discussions. The device is the drinking bird that would be a good imitation of a perpetual mobile machine, were it possible. The principles that govern the operation of the drinking bird have been discussed in this Journal (1-3) and elsewhere (4, 5). The aims of this article are to describe the operation of the drinking bird in quantitative terms, which was not done before, and to show the similarities between heat engines and the bird. How Does It Work? Figure 1 illustrates the drinking bird, the body of which
contains a volatile liquid and its vapor. This is a single component, two-phase system with only one degree of freedom. For such a system vapor pressure and temperature ~ eiven one, the other mav he cannot v a indeoendentlv: calculated from the ~lausi"s-Clapeyroi equation. When the beak is dry, temperature is uniform throughout the bird, and the vapor pressure in the top chamber must be equal to that in the bottom chamber. The situation chances once the beak is moistened. As the water from the beak evaporates, it extracts heat from the top chamber of the bird. (Heat is also absorbed from the surroundine air. but that does not affect the operation of the bird.) As consequence, the tem~eratureinside the too chamber falls. This leads to (1)lowering of the pressure in the top chamber, (2) a pres-
a
sure gradient between the two chambers, and (3)elevation of the liquid column. As the evaporation from the beak proceeds, the pressure in the top chamber continues to fall and the liquid column continues to rise. The rise in the liquid column is arrested by the bird tipping when its center of gravity, which rises as the liquid column rises, falls outside the stem. At this moment there is a break in the liquid column, and contact is established between the two chambers. Thus the vapor pressure and tem~eraturewain become uniform throuehout the vold it returns to the originalv&tical configume of the bird, a uration. The cycle repeats since evaporation from the beak continues unhindered The Carnot Elflclency ot the Drlnklng Blrd
From the above description it follows that the drinking bird is a heat engine that converts heat of evaporation into work through rotational motion. The "fuel" for this work haDDens to he water that undereoes no chemical transformati; Like other heat engines ihis machine performs work because of the temperature difference between the heat source and the heat sink. The source in this case, however, is at the ambient tem~eratureand the sink (water on the beak) is at a lower tempeiature. One of the fascinating aspects of thermodynamics is that it allows us to estimate the upper limit for efficiency of any
Flgure 2. Thermodynamic cycle fw the drinking bird on a FSplane. The area bounded by Me cycle equals heat absabed by the system per cycle.
Figure 1. Some of me poshlornof medrlnklngbird. (A), (6).and (C)comespond to me positions of Me bird at points a, b. and 2 respectively, in the cycles shown in Figures 2 and 3.
Figure 3. m o d y n a m i c cycle for the drlnking blrd on a P-Vplane. The area bounded by the cycle equals work done by lhe system.
Volume 67 Number 6 June 1990
457
machine even when nothing is known about the details of its o ~ e r a t i o nor of the nature of the chemical transformations. 1; order to do this, one assumes that the operations are carried out in such a way that a t any moment equilibrium prevails between the system and the surroundings (reversible process) and throughout the system. The distinction between the system and the surroundings is crucial to thermodynamic analysis; when this distinction is not made, theorv could lead to futile exercises. We mav, .. however, define the system and its boundaries quite arhitrarily as long as we are consistent. What is the svstem here? Since the vapor in the upper chamber undergo& expansion and compression during the o~erations,we have to consider the vapor in the uppe;chamber to b e t h e system. I t is true that after each cycle the vapor from this chamber mixes with the vapor from the lower chamher and a different set of molecules form the system. This does not, however, forbid ua from treating the problem as though the working substance is the same in every cycle. Indeed such an assumption is often made when computing the efficiency of heat engines. For example, in the air-standard analysis of the Otto engine (used in gasolinepowered engines, except the rotary type) one assumes the same gas mixture is repeatedly used even though, in the actual ooeration. fresh fuel is introduced in each cycle (6). The choice of the system in thermodynamics, ulti&ately, is dicrated by the properties we are interested in studying and not necessarily by the physical boundaries. The Carnot efficiency, e, is given by ~
~
.
~~
where the subscripts 1 and 2 refer to the lowest and the highest temperatures, respectively, for the vapor in the upper chamber. The highest temperature is the same as that of the lower chamber. which is the ambient temperature. The , pressure at pressure in the top chamber changes from P ~
